Universiteit van Amsterdam


Institute for Logic, Language and Computation

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17 September 2003, Some remarks about canonical completions of lattices and some
remarks about the orthomodular law.,
Prof. John Harding

Speaker: Prof. John Harding (New Mexico State University)
Date: Wednesday 17 September 2003
Time: 16:00-18:00
Location: Room P.019, Euclides Building, Plantage Muidergracht 24, Amsterdam

This talk has two largely unrelated components. The first is a discussion of canonical completions of bounded lattices with additional operations. In joint work with Mai Gehrke, we have formed a reasonably well-developed theory of a completion for arbitrary bounded lattices that reduces in the Boolean setting to the embedding of a Boolean algebra into the power set of its Stone space. We give an overview of results in this area including recent work with Yde Venema relating canonical completions to MacNeille completions.

The second component of this talk discusses some recent developments regarding the motivation behind the orthomodular law. We review some of the historical developments that lead to introduction of the orthomodular law beginning with the classic Birkhoff von Neumann paper suggesting modular ortholattices rather than Boolean algebras might be the appropriate vehicle to capture the logic of a quantum mechanical system where "incompatible" propositions are present. We discuss how this was refined to the notion of orthomodular lattices in an attempt to capture the essential features arising from the Hilbert space theory used by von Neumann to model quantum mechanics. The body of our efforts lie in showing that the orthomodular law has much more primitive motivations, and that these more primitive motivations also underlie the occurence of the orthomodular law in Hilbert space theory.

Please note that this newsitem has been archived, and may contain outdated information or links.